Fourier series example: the triangle wave | Lecture 51 | Differential Equations for Engineers

[@ProfJeffreyChasnov]

Find other Differential Equations videos in my playlist kzbin.info/aero/PLkZjai-2JcxlvaV9EUgtHj1KV7THMPw1w

[@guillemllodra7304]

Why ao is equal to 0?

[@georgetait386]

as when n = zero, a0 = int_0^pi ( 1- 2x/pi)dx = (x - x^2/pi) , evaluated at zero and pi. at zero its obviously going to be zero, at pi you get pi - pi^2/pi = pi - pi = 0 Hard to write maths in YT comments lol

[@edwardrhodes4403]

If i had this same triangular wave but instead of being 1 at 0 it was 0 at 0 (so it would be a sine equivalent rather than a cos equivalent wave), is there an easy way to convert this?

[@haya4895]

thank you alot, this is helpful. a question here, because you only got half of the period interval from 0 to pi, should you multiply the final result with 2? to represent the whole period?

[@JrgenHelland00]

I believe he has done that. Check out the previous video where he derives these formulas.

[@haya4895]

@@JrgenHelland00 thank you!

[@dominicellis1867]

Typical engineering lecture: this integral is left for the reader lol. This ends up being the Mellin transform of cosine evaluated at s = 0 and s = 1. Is there a way to use analysis to describe the sound that the triangle wave sounds like?

[@lucieneyvrard5414]

Hi guys I’m a bit confuse I found - 4/pi^2n^2 ... but why it is 1- cos (npi ) If any can explain it would be great

[@abhipsosarchives1134]

how is the function even

[@matthewrayner571]

Late reply, and hopefully you've sorted this question out, but here goes. We use "even" and "odd" to describe functions as well as numbers. It's dumb. An even function doesn't care if you put in the negative of your number i.e. f(x) = f(-x) An odd number goes flips the sign if you put in the negative of your number i.e. f(-x) = -f(x) That's all he means. By exploiting the fact that we know we want an even function, we can ignore all the sine terms in the Fourier series (all the odd ones).

[@NikodAnimations]

Tried in desmos. Doesn't work.

[@mateom7201]

Why do you just “look at the answer” and not show how to do it? That’s the whole point of this video

[@johnnyd.j.6068]

i just realized this man is writing backwards

[@bigulf4872]

i think the video's just flipped my guy

[@RT710.]

@@bigulf4872 this is the reciprocal video